Question

If Rolle's theorem is applicable to the function $f\left(x\right)=\frac{\ell nx}{x},(x>0)$ over the interval $[a,b]$ where $aϵI,bϵI$, then the value of $a^2+b^2$ can be

• A. $20$
• B. $25$
• C. $45$
• D. $10$

Answer 1

The correct option is A $20$

Rolle's Theorem is applicable

$f\left(x\right)=\frac{lnx}{x}[a,b]$

$f\left(a\right)=f\left(b\right)$....... $a\ne b$

$\frac{lna}{a}=\frac{lnb}{b}$

$blna=alnb$

$a^b=b^a$

$2^4=4^2$ where $a=2$ & $b=4$

$a^2+b^2=4+16=20$